On product-one sequences over dihedral groups

On the Vertices of Indecomposable Modules over Dihedral 2-groups

Let k be an algebraically closed field of characteristic 2. We calculate the vertices of all indecomposable kD8-modules for the dihedral group D8 of order 8. We also give a conjectural formula of the induced module of a string module from kT0 to kG where G is a dihedral group G of order ≥ 8 and where T0 is a dihedral subgroup of index 2 of G. Some cases where we verified this formula are given.

On Hamilton Circuits in Cayley Digraphs over Generalized Dihedral Groups

In this paper we prove that given a generalized dihedral group DH and a generating subset S, if S∩H 6= ∅ then the Cayley digraph → Cay(DH , S) is Hamiltonian. The proof we provide is via a recursive algorithm that produces a Hamilton circuit in the digraph.

On the eigenvalues of Cayley graphs on generalized dihedral groups

‎Let $Gamma$ be a graph with adjacency eigenvalues $lambda_1leqlambda_2leqldotsleqlambda_n$‎. ‎Then the energy of‎ ‎$Gamma$‎, ‎a concept defined in 1978 by Gutman‎, ‎is defined as $mathcal{E}(G)=sum_{i=1}^n|lambda_i|$‎. ‎Also‎ ‎the Estrada index of $Gamma$‎, ‎which is defined in 2000 by Ernesto Estrada‎, ‎is defined as $EE(Gamma)=sum_{i=1}^ne^{lambda_i}$‎. ‎In this paper‎, ‎we compute the eigen...

Dihedral Groups

A large family of cospectral Cayley graphs over dihedral groups

The adjacency spectrum of a graph Γ , which is denoted by Spec(Γ ), is the multiset of eigenvalues of its adjacency matrix. We say that two graphs Γ and Γ ′ are cospectral if Spec(Γ ) = Spec(Γ ). In this paper for each prime number p, p ≥ 23, we construct a large family of cospectral non-isomorphic Cayley graphs over the dihedral group of order 2p. © 2016 Elsevier B.V. All rights reserved.